7 citations · 14 across the 8 of their papers we have counts for
8 papers
Wave-Current-Bathymetry Interaction Revisited: Modeling, Analysis and Asymptotics
Adrian Kirkeby, Trygve Halsne
Starting from the free surface Euler equations, we derive a leading-order system in terms of surface variables, depending on the surface current and on the bathymetry through the d…
Imaging of seabed topography from the scattering of water waves
Adrian Kirkeby
We consider the problem of reconstructing the seabed topography from observations of surface gravity waves. We formulate the problem as a classical inverse scattering problem using…
Unique continuation for water waves and dispersive multiplier equations
Adrian Kirkeby
We show that if a solution to the water wave equation, for an arbitrary short time interval, is flat on an open set and the horizontal fluid velocity at the surface is zero on the…
Feynman's inverse problem
Adrian Kirkeby
We analyse an inverse problem for water waves posed by Richard Feynman in the BBC documentary Fun to Imagine. The problem can be modelled as an inverse Cauchy problem for gravity-c…
Exact and approximate solutions to the Helmholtz, Schrödinger and wave equation in with radial data
Adrian Kirkeby
We derive simple-to-evaluate, closed-form solutions to the inhomogeneous Helmholtz equation, , the Schrödinger equation, $i\hbar \partial_t u + \frac{\…
Feasibility of Acousto-Electric Tomography
Bjørn Jensen, Adrian Kirkeby, Kim Knudsen
In acousto-electric tomography the goal is to reconstruct the electric conductivity in a domain from electrostatic boundary measurements of corresponding currents and voltages, whi…
Photo-acoustic tomography in a rotating setting
Guillaume Bal, Adrian Kirkeby
Photo-acoustic tomography is a coupled-physics (hybrid) medical imaging modality that aims to reconstruct optical parameters in biological tissues from ultrasound measurements. As…
Stable source reconstruction from a finite number of measurements in the Multi-frequency Inverse Source Problem
Mirza Karamehmedović, Adrian Kirkeby, Kim Knudsen
We consider the multi-frequency inverse source problem for the scalar Helmholtz equation in the plane. The goal is to reconstruct the source term in the equation from measurements…